Synopsis

  The casque associated with Image 4 and Verse 4 was buried in the Greek Cultural Garden in Cleveland, OH, somewhere in the near vicinity of these coordinates: 41°31'40.0"N  81°37'35.6"W.

  Unfortunately, we don't have a complete understanding of how this puzzle was meant to work.  It would be very helpful if we could add more detail to this solution so searchers can apply a similar viewpoint to the remaining puzzles. 

Detailed Solution

The solution given below will present clues from the verse and the image in a way that narrows down the search area to that specific point.  Bits of the original image are shown in the left column in cells with a tan background.  Lines from the verse are in the same column but with a yellow background.  (For more detail about any particular clue, check the page for the image or verse.)
Clues		Interpretations
		The shape to the left of the monument suggests that we should be looking in Ohio, possibly near a major highway.
1) Beneath two countries		The casque was buried in the Grecian Cultural Garden, on the side facing the Italian Garden.
2) As the road curves		Parkgate Avenue curves around this section of the gardens.
3) In a rectangular plot 4) Beneath the tenth stone 5) From right to left 6) Beneath the ninth row from the top 7) Of the wall including small bricks 8) Seven steps up you can hop 9) From the bottom level		These are explicit directions to follow up the hill to the back of the wall in the Grecian Garden, where there is a sunken planter at the location specified by the verse.
10) Socrates, Pindar, Apelles		These names, among those of many other luminaries of ancient Greece, are chiseled into the Pylon Monument.
11) Free Speech, couplet, birch		Refers, respectively, to Socrates (died for free speech), Pindar (a poet), and Apelles (a painter; "birch brush").
12) To find casque's destination 13) Seek the columns 14) For the search.		The entrance to the Grecian Garden is marked by two columns that appear in Image 4.
Final Location: 41°31'40.0"N  81°37'35.6"W (Latitude: 41.527774, Longitude: 81.626567)

Step by Step Directions:

1. From the image, use coordinates, 41 and 81 to identify Cleveland, Ohio.
2. From the image, use the silhouette of the Terminal Tower as a landmark.
3. Somehow discover the Cultural Gardens, located 6 miles north on Superior Avenue. 
4. Look at the map of the Cultural Gardens and notice a "road curves" from line 2 of the poem, which is Parkgate Avenue.
5. The Greek Cultural Gardens include features like the:
1. Pylon Monument - shown in the image and referenced on poem line 10
2. Columns - shown in the image and referenced on poem line 13
6. Follow poem lines 3 through 9 to reach the specific location of the planter box where the casque is buried.
7.